# precalculus

posted by .

To what interval I must we restrict the parameter t if the graph of the parametric equations

x=t+1
y = 2t^2 +1

for t in the set I

is identical to the graph of the parametric equations

x = 1+ sin s
y = 2- cos(2s)

for s in [0,pi)?

• precalculus -

it appears we need
1+t = 1+sin s,so
t = sin s
t must be in [0,1] if s is in [0,pi)

also,
2t^2+1 = 2-cos(2s)
2t^2+1 = 2 - (1-2sin^2 s)
2t^2+1 = 2sin^2 s + 1
same domain.

• precalculus -

Thx!

## Similar Questions

1. ### Precalculus

Let G be the graph of the parametric equations x=cos(4t)and y=sin(6t). What is the length of the smallest interval I such that the graph of these equations for all t in I produces the entire graph G?
2. ### Precalculus

Find the sum of all possible values of the constant k such that the graph of the parametric equations x=2+4cos(s) and y=k-4sin(s) intersects the graph of the parametric equations x=1+cos(t) and y=-3+sin(t) at only one point.
3. ### Precalculus

Find the sum of all possible values of the constant k such that the graph of the parametric equations x=2+4cos(s) and y=k-4sin(s) intersects the graph of the parametric equations x=1+cos(t) and y=-3+sin(t) at only one point.
4. ### Precalculus

Let G be the graph of the parametric equations x=cos(4t)and y=sin(6t). What is the length of the smallest interval I such that the graph of these equations for all t in I produces the entire graph G?
5. ### Math: Parametric Equations

Let G be the graph of the parametric equations x = cos(4t), y = sin(6t). What is the length of the smallest interval P such that the graph of these equations for all t E P produces the entire graph G?
6. ### Precalculus

The graph of the parametric equations x=cos(t), y=sin(t) meets the graph of the parametric equations x=2+4cos(s), y=3+4sin(s), at two points. Find the slope of the line between these two points.
7. ### Math: Parametric Equations

The graph of the parametric equations x=cos(t) y=sin(t) meets the graph of the parametric equations x=2+4cos(s) y=3+4sin(s) at two points. Find the slope of the line between these two points. So far I've set up the system of equations …
8. ### Parametric Equations

For the set of parametric equations x = 2t+1 and y = t^2-5, name the initial point on the graph on the interval -5<t<5. a. (-9, -30) b. ( -5, 5) c. (11, 20) d. (-9, 20) (I chose this one)
9. ### Precalculus

Let $\mathcal{G}$ be the graph of the parametric equations \begin{align*} x &= \cos(4t),\\ y &= \sin(6t). \end{align*}What is the length of the smallest interval $I$ such that the graph of these equations for all $t\in I$ produces …
10. ### Precalculus

Let $\mathcal{G}$ be the graph of the parametric equations \begin{align*} x &= \cos(4t),\\ y &= \sin(6t). \end{align*}What is the length of the smallest interval $I$ such that the graph of these equations for all $t\in I$ produces …

More Similar Questions